Crazy functions
Himmelblau’s function
\(f(x, y) = (x^{2} + y - 11)^{2} + (x + y^{2} - 7)^{2}\)
Local minima:
\(f(3.0, 2.0) = 0\)
\(f(-2.805118, 3.131312) = 0\)
\(f(-3.779310, -3.283186) = 0\)
\(f(3.584428, -1.848126) = 0\)
Eggholder function
\(f(x, y) = -(y + 47) \cdot sin(\sqrt{|y + \frac{x}{2} + 47}) - x \cdot sin(\sqrt{|x - (y + 47)|}\)
Global minimum: \((x, y) = (512, 404.2319)\)
Rastrigin function
\(f(x, y) = 20 + x^{2} - 10 \cdot cos(2 \pi x) + y^{2} - 10 \cdot cos(2 \pi y)\)
Global minimum: \((x, y) = (0, 0)\)
Schaffer function N. 2
\(f(x, y) = 0.5 + \frac{sin^{2}(x^{2}-y^{2}-0.5)}{[1 + 0.001\cdot(x^{2} + y^{2})]^{2}}\)
Global minimum: \((x, y) = (0, 0)\)
More
More test functions for optimization: https://en.wikipedia.org/wiki/Test_functions_for_optimization.